Let T : Λ → Λ be an expanding map on a Cantor set. For each suitably normalized Hölder continuous potential, we construct a spectral triple from which one may recover the associated Gibbs measure as a noncommutative measure.

In this paper we introduce the curvature of densely defined universal connections on Hilbert C⁎-modules relative to a spectral triple (or unbounded Kasparov module), obtaining well-defined operator. Fixing triple, find that modulo junk forms, only depends represented form connection. We refine our definition factorizations modules. Our recovers all data Riemannian submersion compact manifolds, ...

We explore the role played by the spectral curves associated with Higgs pairs in the context of the Nahm transform of doubly-periodic instantons previously defined by the author. More precisely, we show how to construct a triple consisting of an algebraic curve plus a line bundle with connection over it from a doubly-periodic instanton, and that these coincide with the Hitchin’s spectral data a...

Height time hyperspectral near IR probing providing broad-band coverage is employed on PbSe nanocrystals, uncovering spectral evolution following high energy photo-excitation due to hot exciton relaxation and recombination. Separation of single, double and triple exciton state contributions to these spectra is demonstrated, and the mechanisms underlying the course of spectral evolution are inve...

This paper establishes a link between Noncommutative Geometry and canonical quantum gravity. A semi-finite spectral triple over a space of connections is presented. The triple involves an algebra of holonomy loops and a Dirac type operator which resembles a global functional derivation operator. The interaction between the Dirac operator and the algebra reproduces the Poisson structure of Gener...

Abstract. We study countable sums of two dimensional modules for the continuous complex functions on a compact metric space and show that it is possible to construct a spectral triple which gives the original metric back. This spectral triple will be finitely summable for any positive parameter. We also construct a sum of two dimensional modules which reflects some aspects of the topological di...

While there has been growing interest for noncommutative spaces in recent times, most examples have been based on the simplest noncommutative algebra: [xi, xj ] = iθij . Here we present new classes of (non-formal) deformed products associated to linear Lie algebras of the kind [xi, xj ] = ic k ijxk. For all possible threedimensional cases, we define a new star product and discuss its properties...

The Sierpinski gasket admits a locally isometric ramified self-covering. A semifinite spectral triple is constructed on the resulting solenoidal space, and its main geometrical features are discussed.

It is known that the spin structure on a Riemannian manifold can be extended to noncommutative geometry using the notion of a spectral triple. For finite geometries, the corresponding finite spectral triples are completely described in terms of matrices and classified using diagrams. When tensorized with the ordinary space-time geometry, finite spectral triples give rise to Yang-Mills theories ...